Question

a spherical water tank has a radius of 37 feet. can it hold enough water to fill a swimming pool 50 meters long and 20 meters wide to a constant depth of 7 meters? the spherical water tank holds □ ft³ which is enough water to fill the swimming pool, because the pool requires □ ft³ to fill to the desired depth. (round to the nearest integer as needed.)

Explanation:

Step1: Calculate volume of spherical tank

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$. Given $r = 37$ feet, we have $V=\frac{4}{3}\pi(37)^{3}=\frac{4}{3}\pi\times50653\approx\frac{202612\pi}{3}\approx212718.6$ $ft^{3}$.

Step2: Calculate volume of swimming - pool

The swimming - pool is a rectangular prism with length $l = 50$ meters, width $w = 20$ meters and depth $h = 7$ meters. First convert meters to feet. Since 1 meter $\approx3.28084$ feet, $l = 50\times3.28084=164.042$ feet, $w = 20\times3.28084 = 65.6168$ feet, $h = 7\times3.28084=22.96588$ feet. The volume of the rectangular prism $V_{pool}=l\times w\times h=164.042\times65.6168\times22.96588\approx164.042\times65.6168\times22.97\approx164.042\times1518.11\approx248024.7$ $ft^{3}$.

Step3: Compare volumes

Since $212718.6<248024.7$, the spherical tank does not have enough water.

Answer:

The spherical water tank holds $212719$ $ft^{3}$ (rounded to the nearest integer), is not enough water to fill the swimming pool, because the pool requires $248025$ $ft^{3}$ (rounded to the nearest integer).